Lai & Howell
RUME 2014 – Handout
MKT Tasks as Representations of Practice
MKT Tasks as Representations of Practice for
Undergraduate Preparation of Secondary Mathematics Teachers
RESEARCH QUESTIONS: Considering tasks assessing mathematical knowledge for teaching as
representations of mathematics teaching practice:
• What are instructional purposes of teacher education towards which such representations of
practice can or could be used?
• How does pedagogical context, as embedded in a representation of practice, interact with
movement toward an instructional purpose of teacher education?
EXAMPLE TASK ASSESSING MATHEMATICAL KNOWLEDGE FOR TEACHING (MKT TASK):
During a lesson on solving multistep equations, Ms. Kane asked her students to solve the
equation –5x + 8 = 13x – 10. While walking around the classroom looking at what the students
were writing, she noticed several different strategies. For each of the following student
solutions, indicate whether or not the work provides evidence that the student is reasoning
correctly about this problem.
Provides
Evidence of Correct
Student Reasoning
Does Not Provide
Evidence of Correct
Student Reasoning
(A)
(B)
(C)
(D)
© 2012 Bill & Melinda Gates Foundation and Educational Testing Service, all rights reserved.
Yvonne Lai – [email protected]
University of Nebraska-Lincoln
Heather Howell – [email protected]
Educational Testing Service
Please do not cite or distribute without permission
Lai & Howell
RUME 2014 – Handout
MKT Tasks as Representations of Practice
KEY REFERENCES
REPRESENTATIONS OF PRACTICE AND TEACHER EDUCATION
•
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009).
Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
•
Shulman, L.S. (1998). Theory, practice, and the education of professionals. The Elementary
School Journal, 98(5), 511-526.
MKT, DEVELOPMENT AND ANALYSIS OF INSTRUMENTS ASSESSING MKT
•
•
•
•
•
•
•
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it
special? Journal of Teacher Education, 59(5), 389-407. Retrieved from
http://dx.doi.org/10.1177/0022487108324554
Herbst, P. & Kosko, K. (2012). Mathematical knowledge for teaching high school geometry. Paper
presented at the 34th Annual Meeting of the North American Chapter of the International Group
for the Psychology of Mathematics Education. Kalamazoo, MI: PME-NA.
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics
knowledge for teaching. Elementary School Journal, 105, 11-30. Retrieved from
http://dx.doi.org/10.1086/428763
Phelps, G., Howell, H., & Kirui, D. (2013). Assessing content knowledge for teaching: Situating
knowledge assessment in teaching practice. Manuscript in preparation. (Please contact Heather
Howell for the current version of the manuscript; this reference and the one following were used
to construct the coding framework for pedagogical context of MKT tasks.)
Lai, Y., Jacobson, E., & Thames, M. (2013). The role of pedagogical context in measures of specialized
and pedagogical content knowledge. Paper presented at the meeting of the American Educational
Research Association. (Please contact Yvonne Lai for a copy of the paper or for the slides for this
talk; this reference and the one above were used to construct the coding framework for
pedagogical context of MKT tasks.)
Learning Mathematics for Teaching. (2008). Mathematical Knowledge for Teaching (MKT) Measures:
Mathematics Released Items. Author: Ann Arbor, MI.
Phelps, G., & Gitomer, D. (2012). Content knowledge for Teaching Mathematics Grades 4-5
assessment [Measures of Effective Teaching Project]. Unpublished instrument. (Please contact
Heather Howell about obtaining a copy of these released items.)
TEACHING AND INSTRUCTION
•
•
•
Cohen, D. K., Raudenbush, S., & Ball, D. L. (2002). Resources, instruction, and research. In F.
Mosteller & R. Boruch (Eds.), Evidence matters: Randomized trials in education research (pp.80-119).
Washington, DC: Brookings Institution Press. Retrieved from
http://dx.doi.org/10.1029/2001WR000300
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students‘
learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp.
371-404). Charlotte, NC: Information Age Publishers.
Sleep, L. (2012). The work of steering instruction toward the mathematical point: A
decomposition of teaching practice. American Educational Research Journal, 49(5), 935-970.
Yvonne Lai – [email protected]
University of Nebraska-Lincoln
Heather Howell – [email protected]
Educational Testing Service
Please do not cite or distribute without permission